Binary Polar Codes are Optimized Codes for Bitwise Multistage Decoding

TL;DR

This paper reveals that binary polar codes are equivalent to optimized codes for bitwise multistage decoding, unifying two previously known coding schemes and clarifying their relationship.

Contribution

It establishes the equivalence between polar codes and OCBM codes, linking their construction and decoding methods for the first time.

Findings

Binary polar codes are equivalent to OCBM codes.

The techniques for construction and decoding are shown to be the same.

Unifies two previously known coding schemes.

Abstract

Polar codes are considered the latest major breakthrough in coding theory. Polar codes were introduced by Ar{\i}kan in 2008. In this letter, we show that the binary polar codes are the same as the optimized codes for bitwise multistage decoding (OCBM), which have been discovered before by Stolte in 2002. The equivalence between the techniques used for the constructions and decodings of both codes is established.